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#LyX 2.1 created this file. For more info see http://www.lyx.org/
\lyxformat 474
\begin_document
\begin_header
\textclass article
\begin_preamble
% for subfigures/subtables
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\begin_body
\begin_layout Title
Reaching The Ground With Lightning (draft 0.2)
\end_layout
\begin_layout Author
Rusty Russell <[email protected]>
\end_layout
\begin_layout Abstract
The Lightning Network (as proposed by Joseph Poon and Thaddeus Dryja
\begin_inset CommandInset citation
LatexCommand cite
key "Poon2015Lightning"
\end_inset
) requires some new sighash modes in order to work with Bitcoin.
This paper proposes a simplified variant which requires only modifications
which are already proposed for bitcoin, and slightly simplifies the revocation
of existing contracts.
\end_layout
\begin_layout Abstract
Keywords: bitcoin, lightning, revocation hash, HTLC, BIP62, BIP65, BIP68
\end_layout
\begin_layout Section
Introduction
\end_layout
\begin_layout Standard
The Bitcoin network
\begin_inset CommandInset citation
LatexCommand cite
key "nakamoto2008bitcoin"
\end_inset
allows the transfer of value between peers using
\emph on
transactions.
\emph default
Each bitcoin transaction consists of one or more
\emph on
outputs
\emph default
(typically specifying the hash of the recipient's key), and one or more
\emph on
inputs
\emph default
(typically containing the recipient's key and a signature of the transaction).
Thus one transfers value to another peer by creating a transaction which
\emph on
spends
\emph default
one or more outputs and creates an output which the recipient can spend
using their private key.
\end_layout
\begin_layout Standard
While such cryptographic transfer of value is near-instantaneous, ensuring
that the transaction has been included in the consensus of the shared ledger
(aka.
\emph on
blockchain
\emph default
) creates delays ranging from a few minutes to hours, depending on the level
of reliability required.
Inclusion in the blockchain is performed by miners, who preferentially
include transactions paying greatest fee per byte.
\end_layout
\begin_layout Standard
Thus using the blockchain directly is slow, and too expensive for genuinely
small transfers (typical fees are a few cents).
\end_layout
\begin_layout Section
Previous Work
\end_layout
\begin_layout Standard
To work around the bitcoin network's delays and fees, several forms of
\emph on
off-chain
\emph default
transaction patterns have been developed, where series of transactions
are sent directly between two parties, with only the initial opening transactio
n and final redemption transaction being included in the bitcoin blockchain.
\end_layout
\begin_layout Standard
The Lightning Network paper proposed a solution, but at the cost of introducing
new signature variants (sighash ops).
Adding a new signature opcode would allow many other improvements
\begin_inset Foot
status collapsed
\begin_layout Plain Layout
Schnorr signatures offer faster batch validation, according to
https://elementsproject.org/elements/schnorr-signatures/
\end_layout
\end_inset
\begin_inset Foot
status collapsed
\begin_layout Plain Layout
DER encoding adds unnecessary bytes and is a cause of malleability
\end_layout
\end_inset
but that is precisely why it's a matter for longer term research and unlikely
to be deployed in Bitcoin in the immediate future.
\end_layout
\begin_layout Subsection
Payment Channels
\end_layout
\begin_layout Standard
The concept of
\emph on
payment channels
\emph default
(sometimes called micropayment channels) has existed in various forms for
several years
\begin_inset CommandInset citation
LatexCommand cite
key "BitcoinChannels"
\end_inset
.
The simplest form is as follows, and allows A to quickly and cheaply pay
B a stream of slightly increasing amounts:
\end_layout
\begin_layout Enumerate
A creates an
\emph on
anchor
\emph default
transaction to
\emph on
open the channel
\emph default
which:
\end_layout
\begin_deeper
\begin_layout Enumerate
Outputs $1,
\end_layout
\begin_layout Enumerate
Requires the signatures of both A and B to redeem.
\end_layout
\end_deeper
\begin_layout Enumerate
A sends the transaction ID of the anchor, which output to spend, and the
amount of that output to B.
\end_layout
\begin_layout Enumerate
B signs a
\begin_inset Quotes eld
\end_inset
refund
\begin_inset Quotes erd
\end_inset
transaction which:
\end_layout
\begin_deeper
\begin_layout Enumerate
spends that anchor output,
\end_layout
\begin_layout Enumerate
outputs the $1 to an address controlled by A, and
\end_layout
\begin_layout Enumerate
can only be spent in 24 hours (using the
\emph on
locktime
\emph default
field)
\end_layout
\end_deeper
\begin_layout Enumerate
B sends A the refund transaction.
\end_layout
\begin_layout Enumerate
A broadcasts the anchor transaction, knowing she can get the funds back
in 24 hours using the refund if B vanishes.
\end_layout
\begin_layout Standard
A can now pay B 1 cent by signing a new
\emph on
commitment
\emph default
transaction to send to B, which spends the anchor output and has two outputs:
one pays A 99c, and the other pays B 1 cent.
A can later pay B another cent by signing another transaction (
\begin_inset Quotes eld
\end_inset
updating the commitment
\begin_inset Quotes erd
\end_inset
) for B which pays A 98c and B 2c, etc.
\end_layout
\begin_layout Standard
At any point, B can
\begin_inset Quotes eld
\end_inset
close the channel
\begin_inset Quotes erd
\end_inset
by signing and broadcasting the latest commitment transaction to collect
the money.
B should do this before 24 hours pass, otherwise A can use the refund transacti
on.
\end_layout
\begin_layout Subsubsection
Limitations Of Simple Payment Channels
\end_layout
\begin_layout Standard
Simple channels have several limitations:
\end_layout
\begin_layout Description
Single
\begin_inset space ~
\end_inset
recipient.
A new recipient requires a new channel, which must wait for consensus on
the anchor transaction.
\end_layout
\begin_layout Description
One
\begin_inset space ~
\end_inset
way.
They cannot be reversed: A can sign a transaction which pays B less money
than the last, but B could still broadcast the older transaction.
\end_layout
\begin_layout Description
Vulnerable
\begin_inset space ~
\end_inset
to
\begin_inset space ~
\end_inset
malleability.
The anchor transaction could be altered in several ways (without invaliding
it completely) before inclusion in the blockchain: this alters its transaction
id and thus makes the refund transaction unusable.
\end_layout
\begin_layout Standard
This last issue is a common one with complex bitcoin transactions, and BIP62
\begin_inset CommandInset citation
LatexCommand cite
key "BIP62"
\end_inset
is proposed to prevent non-signing parties from being able to malleate
transactions.
\end_layout
\begin_layout Subsection
Generalized Payment Channels Using Revocable Transactions
\end_layout
\begin_layout Standard
The Lightning network introduced generalized, bi-directional payment channels,
referred to here as
\emph on
Poon-Dryja channels
\emph default
.
These use a mutual anchor, which both create to provide the channel funding,
and a symmetrical
\emph on
pair
\emph default
of updatable commitment
\emph on
\emph default
transactions rather than the single transaction used in the one-way channel
case, as shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Figure-1-from"
\end_inset
\begin_inset Foot
status collapsed
\begin_layout Plain Layout
Note: this diagram has been corrected since: Commitment Close Tx 1A (CC1b)
-- should be CC1a, and vice-versa
\end_layout
\end_inset
.
\end_layout
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open
\begin_layout Plain Layout
\align center
\begin_inset Graphics
filename ln-draft-fig1.eps
scale 50
\end_inset
\end_layout
\begin_layout Plain Layout
\begin_inset Caption Standard
\begin_layout Plain Layout
Figure 1 from the Lightning Network Draft 0.5
\begin_inset CommandInset label
LatexCommand label
name "fig:Figure-1-from"
\end_inset
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Standard
To update the commitment, A sends B a signature for B's new commitment transacti
on, and B sends A a signature for A's new commitment transaction.
\end_layout
\begin_layout Standard
As before, each commitment transaction contains two outputs, one for A and
one for B; but A's commitment transaction output to itself is encumbered
by an additional restriction (as is B's output to itself).
Instead of paying A directly, A's output needs both A and B's signature.
B provides such a signature, but on a
\begin_inset Quotes eld
\end_inset
commitment refund
\begin_inset Quotes erd
\end_inset
transaction which can only be spent after a delay (40 days in the paper).
Thus if A closes the channel by signing and broadcasting its commitment
transaction, B can collect its output immediately, but A must wait 40 days.
\end_layout
\begin_layout Standard
This delay encumbering the output is what makes the commitment transaction
\emph on
revocable;
\emph default
once an updated commitment transaction is agreed upon, the previous commitment
transaction pair is revoked by sharing the private keys needed to redeem
those encumbered outputs.
Thus, A shares its (throwaway) private key, and B shares its throwaway
private key.
If A were to sign and broadcast a revoked commitment transaction, B could
not only immediately spend its own output, but it has both A's key and
its own to generate a transaction which can spend the output which would
normally go to A after a delay.
\end_layout
\begin_layout Subsection
Hashed Timelock Contracts (HTLCs)
\end_layout
\begin_layout Standard
The Lightning Network paper used a set of 4 transactions to implement a
\emph on
hashed timelock contract,
\emph default
which guarantees payment of a given amount on presentation of a secret value
\emph on
R
\emph default
within a certain timespan.
Any number of these could be active within a generalized channel, and this
is what allows a network to form: Node A offers node B $1 for the secret
within 2 days, node B offers node C 99c for the secret within 1 day, etc.
\end_layout
\begin_layout Standard
This arrangement for one side of a single node is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Figure-2-from"
\end_inset
.
\end_layout
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open
\begin_layout Plain Layout
\align center
\begin_inset Graphics
filename ln-draft-fig2.eps
scale 50
\end_inset
\end_layout
\begin_layout Plain Layout
\begin_inset Caption Standard
\begin_layout Plain Layout
Figure 2 from the Lightning Network Draft 0.5
\begin_inset CommandInset label
LatexCommand label
name "fig:Figure-2-from"
\end_inset
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Section
Enhancements To Lightning
\end_layout
\begin_layout Standard
This paper proposes various modifications.
\end_layout
\begin_layout Subsection
Poon-Dryja Generalized Payment Channel Modifications
\end_layout
\begin_layout Standard
This paper proposes three changes to the commitment transactions.
\end_layout
\begin_layout Subsubsection
Placing Timeout in Output Script
\end_layout
\begin_layout Standard
Rather than using a separate transaction to enforce the delay, BIP65
\begin_inset CommandInset citation
LatexCommand cite
key "BIP65"
\end_inset
proposes an OP_CHECKLOCKTIMEVERIFY which allows an output to specify the
minimum time at which it can be spent.
With this enhancement, we no longer need a separate
\begin_inset Quotes eld
\end_inset
commitment refund
\begin_inset Quotes erd
\end_inset
transaction.
The commitment transaction to-self output script would be a little more
complex:
\end_layout
\begin_layout Itemize
A and B's signature, OR
\end_layout
\begin_layout Itemize
A's signature and OP_CHECKLOCKTIMEVERIFY <40 days>
\end_layout
\begin_layout Standard
As of Nov.
13, 2015, BIP65 has been deployed and is in the process of being activated.
\end_layout
\begin_layout Subsubsection
Using Relative Locktime
\end_layout
\begin_layout Standard
The Poon-Dryja channel uses a 40 day locktime, because transaction locktime
is absolute.
Before 40 days the channel must be closed, otherwise spending a revoked
transaction and immediately following it with the commit refund transaction
is possible.
\end_layout
\begin_layout Standard
BIP112[#BIP112] proposes OP_CHECKSEQUENCEVERIFY, an opcode which allows
an output to specify a minimum
\emph on
relative
\emph default
time before the output can be spent
\begin_inset CommandInset citation
LatexCommand cite
key "friedenbach_bitcoin-development_2015,BIP112"
\end_inset
can reduce this timeout (say, to 1 day) and avoid placing a lifetime limit
on the channel, like so:
\end_layout
\begin_layout Itemize
A and B's signature, OR
\end_layout
\begin_layout Itemize
A's signature and OP_CHECKSEQUENCEVERIFY <1 day>
\end_layout
\begin_layout Standard
As of Nov.
13, 2015, BIP112 has not been deployed.
\end_layout
\begin_layout Subsubsection
Using Revocation Preimages Instead of Private Keys
\end_layout
\begin_layout Standard
There's a slightly more intuitive and more efficient method than exchanging
private keys, which is to reuse a technique of hash preimages which is
already needed for HTLCs (as we see later).
\end_layout
\begin_layout Standard
Instead of using a private key, B uses knowledge of a hash preimage as well
as its signature to steal funds from a revoked commitment transaction.
Thus, to create a commitment transaction each side provides a hash value;
to revoke a commitment transaction it provides the prehash image.
\end_layout
\begin_layout Standard
The resulting commitment transaction to-self output now looks like:
\end_layout
\begin_layout Itemize
B's signature and a preimage which hashes to <revocation-hash>, OR
\end_layout
\begin_layout Itemize
A's signature and OP_CHECKSEQUENCEVERIFY <1 day>
\end_layout
\begin_layout Standard
This can be expressed fairly easily in bitcoin's script-based scripting
language, as annotated in
\begin_inset CommandInset ref
LatexCommand nameref
reference "sub:Commitment-Outputs-For"
\end_inset
.
The final pair of commitment transaction outputs is shown in Figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Commitment-Transaction-Outputs"
\end_inset
.
\end_layout
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open
\begin_layout Plain Layout
\align center
\begin_inset Graphics
filename commit-tx.eps
scale 50
\end_inset
\end_layout
\begin_layout Plain Layout
\begin_inset Caption Standard
\begin_layout Plain Layout
Commitment Transaction Outputs
\begin_inset CommandInset label
LatexCommand label
name "fig:Commitment-Transaction-Outputs"
\end_inset
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Channel Opening Modifications
\end_layout
\begin_layout Standard
The method of creating the first commitment transaction before signing the
anchor transaction (as proposed in the paper) presents two problems in
practice:
\end_layout
\begin_layout Enumerate
The anchor transaction id required for the commitment input will only be
known once the anchor is signed, and
\end_layout
\begin_layout Enumerate
The anchor transaction can be malleated by either party before entering
the blockchain, rendering the commitment input unusable.
\end_layout
\begin_layout Standard
The last of these is particularly pernicious, as BIP62 doesn't solve it:
signatories can always re-sign a transaction, hence altering its transaction
ID.
The paper proposes new SIGHASH flags which mitigate this problem, but we
are attempting to avoid that.
\end_layout
\begin_layout Standard
Our approach is to only have one-sided anchors.
These can be later balanced by the lightning network itself, or an atomic-swap
to an on-chain bitcoin transaction
\begin_inset CommandInset citation
LatexCommand cite
key "go1111111_single_anchor"
\end_inset
.
Any bitcoin transaction fees are initially funded by that anchor, but the
implementation splits fees where possible and never allows either side
to spend funds in the channel if they would no longer be able to pay their
share.
\end_layout
\begin_layout Subsection
Hashed Timelock Contract (HTLC) Modification
\end_layout
\begin_layout Standard
Using the same techniques used above, we can condense each HTLC into a single
output script on the commitment transaction.
This output is spendable under three conditions:
\end_layout
\begin_layout Enumerate
Recipient knows the R value (funds go to recipient), or
\end_layout
\begin_layout Enumerate
The HTLC has timed out (funds return to sender), or
\end_layout
\begin_layout Enumerate
The Commit transaction has been revoked (funds go to other side).
\end_layout
\begin_layout Standard
Unlike the original paper, we use revocation preimages instead of sharing
temporary private keys.
If we also use OP_CHECKLOCKTIMEVERIFY and OP_CHECKSEQUENCEVERIFY it is
fairly simple to express these conditions in a single output script.
\end_layout
\begin_layout Standard
For each direction the HTLC could transfer funds, there are two scripts
required; one for A's commitment transaction and one for B's commitment
transaction.
It's also a requirement that the conditions which allow payment to oneself
be delayed, to give the other side an opportunity to take the funds in
case of revocation.
This is shown (omitting the HTLC to-self delays, which depend on the orientatio
n of payer/payee with respect to A and B) in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:HTLC-Using-Revocation"
\end_inset
.
\end_layout
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open
\begin_layout Plain Layout
\align center
\begin_inset Graphics
filename htlc.eps
scale 50
\end_inset
\end_layout
\begin_layout Plain Layout
\begin_inset Caption Standard
\begin_layout Plain Layout
HTLC Using Revocation Preimages, OP_CLTV and OP_CSV (simplified)
\begin_inset CommandInset label
LatexCommand label
name "fig:HTLC-Using-Revocation"
\end_inset
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Standard
The scripts for this can be found in
\begin_inset CommandInset ref
LatexCommand nameref
reference "sec:Appendix-A:-Scripts"
\end_inset
.
\end_layout
\begin_layout Section
Conclusions
\end_layout
\begin_layout Standard
Secret preimages can replace exposure of temporary private keys in the Lightning
Network constructs with no loss of generality, and a slight gain in simplicity.
\end_layout
\begin_layout Standard
The use of script conditionals to enforce timeouts instead of using separate
pre-signed transactions reduces an HTLC from a set of four dual-signed
transactions to a single (more complex) output script, and additionally
avoids any requirement for new CHECKSIG flags for HTLCs.
\end_layout
\begin_layout Standard
By using a rebalanced single anchor, channel establishment can also avoid
new CHECKSIG flags, though it loses the important ability to outsource
the enforcement of channel contract terms.
\end_layout
\begin_layout Section*
Acknowlegments
\end_layout
\begin_layout Standard
Thanks to mmeijeri on Reddit's r/Bitcoin for pointing out a flaw in escape
transactions reusing the same A and B keys as the commitment transaction
in
\begin_inset CommandInset ref
LatexCommand nameref
reference "sec:Appendix-B:-Dual"
\end_inset
\begin_inset Foot
status open
\begin_layout Plain Layout
https://www.reddit.com/r/Bitcoin/comments/3dlxw4/reaching_the_ground_with_lightnin
g_lightning/ct80xpp
\end_layout
\end_inset
.
Thanks to John Newbery for multiple formatting and typing corrections.
\end_layout
\begin_layout Standard
Thanks to Joseph Poon for designing the escape/fast-escape dual-anchor method,
as well as finding a flaw in my original formulation of the dual anchor
construct and reviewing an earlier draft of this paper.
Also thanks to him and Thaddeus Dryja for the initial eye-opening Lightning
Network paper.
\end_layout
\begin_layout Standard
\begin_inset CommandInset bibtex
LatexCommand bibtex
bibfiles "bitcoin"
options "bibtotoc,plain"
\end_inset
\end_layout
\begin_layout Section*
Appendix A: Transaction Scripts
\begin_inset CommandInset label
LatexCommand label
name "sec:Appendix-A:-Scripts"
\end_inset
\end_layout
\begin_layout Standard
All outputs are expressed as pay-to-scripthash outputs, where the redeeming
input provides the redeemscript.